Federated Learning (FL) allows machine learning models to train locally on individual mobile devices, synchronizing model updates via a shared server. This approach safeguards user privacy; however, it also generates a heterogeneous training environment due to the varying performance capabilities across devices. As a result, straggler devices with lower performance often dictate the overall training time in FL. In this work, we aim to alleviate this performance bottleneck due to stragglers by dynamically balancing the training load across the system. We introduce Invariant Dropout, a method that extracts a sub-model based on the weight update threshold, thereby minimizing potential impacts on accuracy. Building on this dropout technique, we develop an adaptive training framework, Federated Learning using Invariant Dropout (FLuID). FLuID offers a lightweight sub-model extraction to regulate computational intensity, thereby reducing the load on straggler devices without affecting model quality. Our method leverages neuron updates from non-straggler devices to construct a tailored sub-model for each straggler based on client performance profiling. Furthermore, FLuID can dynamically adapt to changes in stragglers as runtime conditions shift. We evaluate FLuID using five real-world mobile clients. The evaluations show that Invariant Dropout maintains baseline model efficiency while alleviating the performance bottleneck of stragglers through a dynamic, runtime approach.